- Comparing decimals: 9.97 and 9.798
- Comparing decimals: 156.378 and 156.348
- Compare decimals through thousandths
- Ordering decimals
- Ordering decimals through thousandths
- Order decimals
- Comparing decimals in different representations
- Comparing decimals word problems
- Compare decimals word problems
Explore the concept of comparing decimals. Learn the importance of aligning place values and starting from the largest place value when comparing. The video also demonstrates that more digits doesn't necessarily mean a larger number.
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- [Lecturer] Al is comparing two recipes for homemade bread. The recipe for white bread calls for 4/10 of a kilogram of flour. The recipe for whole wheat bread calls for 385/1000 of a kilogram of flour. Which bread takes less flour? So the white bread calls for 4/10 of a kilogram, while the recipe of whole wheat bread calls for 0.385 kilograms, or 385/1000 of a kilogram. Now the way I wrote it is important. You always want to line up the decimals when you are comparing, because you want to compare numbers in the same place value. And this is an interesting example of even though the number down here has more digits it doesn't mean that it's necessarily a larger number. What we want to do when we compare numbers and this is true whether we're dealing with decimals or not, is we start in the largest place value. We could start in the ones place, 'cause both of these have zero ones. Then we go one place value down, we go to the tenths place. The white bread, it requires 4/10 of flour while in the whole wheat bread we only have 3/10 of flour. So we can stop right there. This has more tenths than this does. It doesn't matter that this has more hundredths and thousandths. Those are less significant. They don't add up to as much as what we're dealing with when we look just at the tenths place. So because four is greater than three, and we're in the tenths place we know that white bread takes more flour, but we have to be very careful. They said which bread takes less flour? So it's going to be whole wheat bread. Three is less than four. Let's do another one of these. A group of fifth graders kept track of the number of hours they spent working on their science project right? Put the students in order from the least to greatest amount of time spent. The student with the least amount of time should be at the top of the list. So pause this video and see if you can do this. And this is actually a screenshot from the Khan Academy exercise. If you're doing the Khan Academy exercise you'd actually be able to click on these and move them around. But let's compare them. So as I mentioned in the last example, when you're comparing numbers it's good to line up the place values, so let's do that. So Adam is 5.5. Aviv is five, and Jenny is 5.17. So once again, start at the largest place value. Start at the ones. They all have exactly five ones, so then we move to the next place value. In this case, we're going to go to the tenths place. So when we look at the tenths place, interesting things are going on. Aviv has no tenths. It's a blank here, but you could do this as 5.0. So Aviv has the fewest tenths, then comes Jenny with only 1/10 and then Adam has 5/10. So that tells us enough so that we can order the three. We don't even have to look at the hundredths place because the tenths here are different. So the least number of tenths is Aviv, so that's going to be Aviv is the least. They all have the same number of ones, but Aviv has the least tenths. Then comes Jenny. Jenny, once again, they all have the same number of ones but then Jenny has less tenths than Adam, and then comes Adam. Adam has the most tenths. It doesn't matter that Jenny also has 7/100. Notice you could view this as 17/100 which is going to be less than 5/10 which could also be viewed as 50/100. So the general way to think about it, start at the most significant, the largest place value, compare. If things are equal, go to the next place value. When things are different, then you have enough information to start ordering them.